Short Answer: No, they are very similar but are different sizes. Continue reading the long answer for photos and more information.
Longer Answer: C7 bulbs are shorter with smaller diameters than C9s. Both are installed in 18 AWG traditional Christmas light cords. Many of us remember this style of lighting from when we were kids.
Many Christmas displays use both sizes of bulbs, but each bulb has its own type of cord.
This photo shows the relative size differences between glass C7 and C9 bulbs.
Questions about what size bulb/cord you have in your stash?
A C7 bulb has the same sized socket as a nightlight so using a nightlight bulb for reference can help in determining the size of an unmarked cord.